At what part of the mining process are transaction fees actually used?

If I mine in a pool, and withdraw my btc from that pool into my btc wallet, is that where the transaction fee will be initiated? and the transaction fee is not mandatory, but if I want my confirmed btc in my btc wallet quicker I must use a transaction fee?

I still don't understand what the point of them are, even if I won't be using them.

The network has a real tangible cost. Fees pay that cost. Now Satoshi was smart and realized in the beginning the cost of a secure network would be higher than fees can bring in. So that either leaves the network horribly weak and underfunded or fees so excessive nobody wants to use the network. So he created a block subsidy which also solves the problem of initial distribution of coins in a fair manner.

Miner total compensation = subsidy + fees.Currently the subsidy is 50 BTC but that declines over time.Eventually the subsidy will be 0 BTC and long before that it will be <1 BTC.

Today:Miner Total Compensation = 99.9% subsidy + 0.1% fees

Some point in the future:Miner Total Compensation = 50% subsidy + 50% fees

Eventually once all coins are mined:Miner Total Compensation = 0% subsidy + 100% fees